[tex]\log _6(x^{-2}+2)=1[/tex][tex]\log _6(\frac{1}{x^2}^{}+2)=1[/tex]
first the domain of the equation is
The domain would be all the real numbers except 0
now, the solution of the equation is:
[tex]\frac{\ln(\frac{1}{x^2}^{}+2)}{\ln6}=1[/tex][tex]\ln (\frac{1}{x^2}^{}+2)=\ln 6[/tex][tex]\frac{1}{x^2}+2=6^{}[/tex][tex]\frac{1}{x^2}=4[/tex][tex]x^2=\frac{1}{4}[/tex][tex]x=\sqrt[]{\frac{1}{4}}=\pm\frac{1}{2}[/tex]
